Size Effects on Concrete Tensile Fracture Properties: An Interpretation of the Fractal Approach Based on the Aggregate Grading

The fractal approach to the mechanics of materials with disordered microstructure allows an elegant and unified explanation of the size effects the cohesive model parameters (i.e. the tensile strength and the fracture energy) are subjected to.Since, in normal strength concrete, the weakest link is represented by the interfaces between the aggregate and the cement matrix, it seems reasonable to connect the localization of the damage with the aggregate distribution inside concrete.The aim of this work is to show how fractal patterns in the tensile failure of concrete specimens can be derived by the grain size distribution of the aggregates composing the concrete.The most common aggregate grading, the Füller sieve curve, will be considered and expressed in terms of probability density function of the diameter of the grains.It is found that the surface of the aggregate inside the damaged band where the main crack will grow in the last stage of the tensile failure can be modelled by an invasive fractal set of dimension 2.5.By stereology concepts, we obtain also the probability density function of the diameters of the circles interception of the grains with a plane cutting the damaged band; this function shows that the resistant cross section can be modelled by a lacunar fractal set (i.e. with dimension lower than 2).Therefore fractality is proven and consequent size effects on strength and fracture energy can be pointed out.

Abstract licence: CC BY-NC-ND

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